Solve 2y^{-1}u^4*2x^-9u^-7*5yx^7

$$2 y ^ { - 1 } u ^ { 4 } \cdot 2 x ^ { - 9 } u ^ { - 7 } \cdot 5 y x ^ { 7 }$$

Evaluate

$$\frac{20}{x^{2}u^{3}}$$

Solution Steps

Multiply y^{-1} and y to get 1.

$$2u^{4}\times 2x^{-9}u^{-7}\times 5x^{7}$$

To multiply powers of the same base, add their exponents. Add 4 and -7 to get -3.

$$2u^{-3}\times 2x^{-9}\times 5x^{7}$$

To multiply powers of the same base, add their exponents. Add -9 and 7 to get -2.

$$2u^{-3}\times 2x^{-2}\times 5$$

Multiply 2 and 2 to get 4.

$$4u^{-3}x^{-2}\times 5$$

Multiply 4 and 5 to get 20.

$$20u^{-3}x^{-2}$$

Differentiate w.r.t. x

$$-\frac{40}{\left(ux\right)^{3}}$$